# Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

## TL;DR

This paper introduces a simple modification to the amplitude phase-field crystal model that allows precise tuning of defect and interface energies, enhancing its ability to match experimental data and analyze microscopic features.

## Contribution

A new term added to the APFC free energy functional enables controlled adjustment of defect and interface energies without affecting other model features.

## Key findings

- The added term effectively increases defect and interface energies.
- Finite element method with mesh refinement improves simulation accuracy.
- The approach works for various crystal structures in 2D and 3D.

## Abstract

One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.